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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.02428 |
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Table of Contents:
- We determine the logarithmic growth exponents of the $L^p$ norms, $1\le p\le\infty$, of $L^2$-normalized Laplace eigenfunctions on the unit disk, for both Dirichlet and Neumann boundary conditions. We also prove sharp uniform $L^p$ upper and lower bounds for every $L^2$-normalized Dirichlet eigenfunction and every non-constant Neumann eigenfunction $u_λ$ on the disk. The proof uses stationary phase estimates and integral estimates for Bessel functions.